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# What are Barkhausen conditions for Oscillation?

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## Barkhausen stability criteria:The Barkhausen stability criteria is a mathematical requirement used in electronics to predict whether a linear electronic circuit may oscillate. Heinrich Georg Barkhausen ($1881-1956$), a German scientist, proposed it in $1921$. It is commonly utilized in the design of electronic oscillators as well as general negative feedback circuits such as op-amps to keep them from oscillating.Barkhausen Conditions For Oscillation:It asserts that if $\mathrm{A}$ is the gain of the amplifying element in the circuit and $\mathrm{\beta }\left(\mathrm{j\omega }\right)$ is the feedback path transfer function, so $\mathrm{\beta A}$ is the loop gain around the circuit's feedback loop, the circuit will maintain steady-state oscillations only at frequencies for which:The loop gain is equal to one in absolute magnitude, which means that $\left|\mathrm{\beta A}\right|=1$The phase shift through the loop is either zero or an integer multiple of $2\mathrm{\pi }$: $\angle \mathrm{\beta A}=2\mathrm{\pi n},\mathrm{n}=0,1,2,\dots$Barkhausen's criteria is a necessary but not sufficient condition for oscillation: certain circuits meet the requirement but do not oscillate.

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